Optimal surface marker locations for tumor motion estimation in lung cancer radiotherapy

Using fiducial markers on the patient's body surface to predict the tumor location is a widely used approach in lung cancer radiotherapy. The purpose of this work is to propose an algorithm that automatically identifies a sparse set of locations on the patient's surface with the optimal prediction power for the tumor motion. In our algorithm, it is assumed that there is a linear relationship between the surface marker motion and the tumor motion. The sparse selection of markers on the external surface and the linear relationship between the marker motion and the internal tumor motion are represented by a prediction matrix. Such a matrix is determined by solving an optimization problem, where the objective function contains a sparsity term that penalizes the number of markers chosen on the patient's surface. Bregman iteration is used to solve the proposed optimization problem. The performance of our algorithm has been tested on realistic clinical data of four lung cancer patients. Thoracic 4DCT scans with ten phases are used for the study. On a reference phase, a grid of points are casted on the patient's surfaces (except for the patient's back) and propagated to other phases via deformable image registration of the corresponding CT images. Tumor locations at each phase are also manually delineated. We use nine out of ten phases of the 4DCT images to identify a small group of surface markers that are mostly correlated with the motion of the tumor and find the prediction matrix at the same time. The tenth phase is then used to test the accuracy of the prediction. It is found that on average six to seven surface markers are necessary to predict tumor locations with a 3D error of about 1 mm. It is also found that the selected marker locations lie closely in those areas where surface point motion has a large amplitude and a high correlation with the tumor motion. Our method can automatically select sparse locations on the patient's external surface and estimate a correlation matrix based on 4DCT, so that the selected surface locations can be used to place fiducial markers to optimally predict internal tumor motions.